Problem: Divide the polynomials. The form of your answer should either be $p(x)$ or $p(x)+\dfrac{k}{x+1}$ where $p(x)$ is a polynomial and $k$ is an integer. $\dfrac{3x^3+10x^2+7x}{x+1}=$
Usually, there are many different ways to divide polynomials. Here, we will use the method of polynomial long division. Notice that the expression in the numerator is missing a constant (degree $0$ ) term. To avoid any confusion, let's add that term as $0$. $\begin{array}{r} 3x^2+7x+0 \\ x+1|\overline{3x^3+10x^2+7x+0} \\ \mathllap{-(}\underline{3x^3+\phantom{1}3x^2\phantom{+7x+0}\rlap )} \\ 7x^2+7x+0 \\ \mathllap{-(}\underline{7x^2+7x\phantom{+0}\rlap )} \\ 0x+0 \\ \mathllap{-(}\underline{0x+0\rlap )} \\ 0 \end{array}$ We found that the quotient is $3x^2+7x$ and the remainder is $0$, which means the answer is simply a polynomial (no expression of the form $\dfrac{k}{x+1}$ ). $\dfrac{3x^3+10x^2+7x}{x+1}=3x^2+7x$